#numbers — Public Fediverse posts

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

This animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
🧵⬇️

1: The natural numbers (A000027) ➡️ https://decompwlj.com/3DgraphGen/Natural_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A069686: Primes whose internal digits form a prime
A069686 ➡️ https://oeis.org/A069686

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069686.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069686.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069686.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of prime numbers in 3D, threejs - webGL (log(weight), log(level), log(jump))
➡️ https://decompwlj.com/3Dgraph/Prime_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #numbers #primes #PrimeNumbers #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A069346: Primes of the form n - Omega(n), where Omega(n) is the number of prime factors of n, A001222(n)
A069346 ➡️ https://oeis.org/A069346

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069346.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069346.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069346.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

💁🏻‍♀️ ICYMI: 🔢🎲 Mathematician Ben Sparks introduces the 15-game, a two-player number #game where players take turns picking digits from 1 to 9 to reach a sum of 15. He explains how visual #diagrams can simplify complex strategies and change how we approach mathematical problems.

👉 Learn more: https://seethis.tv/post/15-game-mathematical-visualization-numberphile

#dataviz #data #diy #games #howto #math #numbers #patterns #play #shapes #squares #toys #tricks #geometry #puzzles #education #learning #logic #addition #tksst #video

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A069059: Numbers k such that k and sigma(k) are not relatively prime
A069059 ➡️ https://oeis.org/A069059

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069059.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069059.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069059.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) ➡️ https://decompwlj.com/
- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

#decompwlj #math #mathematics #maths #sequence #OEIS #PARIGP #Downloads #Algorithms #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A068781: Lesser of two consecutive numbers each divisible by a square
A068781 ➡️ https://oeis.org/A068781

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068781.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068781.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068781.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A068780: Composite numbers n such that n+1 is also composite
A068780 ➡️ https://oeis.org/A068780

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068780.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068780.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068780.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #numbers #TwinPrimes #twin #primes #conjecture #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A068501: Values m such that the consecutive pair parameters(m,m+1) generate Pythagorean triples whose odd terms are both prime
A068501 ➡️ https://oeis.org/A068501

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068501.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068501.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068501.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

💁🏻‍♀️ NEW: 🔢🎲 Mathematician Ben Sparks introduces the 15-game, a two-player number #game where players take turns picking digits from 1 to 9 to reach a sum of 15. He explains how visual #diagrams can simplify complex strategies and change how we approach mathematical problems.

👉 Learn more: https://seethis.tv/post/15-game-mathematical-visualization-numberphile

#dataviz #data #diy #games #howto #math #numbers #patterns #play #shapes #squares #toys #tricks #geometry #puzzles #education #learning #logic #addition #tksst #video

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A067947: Numbers k such that k divides 7^k - 1
A067947 ➡️ https://oeis.org/A067947

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067947.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067947.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067947.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

A067945: Numbers k that divide 3^k - 1
A067945 ➡️ https://oeis.org/A067945

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067945.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067945.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067945.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A067889: Primes sandwiched between two numbers having same number of divisors
A067889 ➡️ https://oeis.org/A067889

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067889.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067889.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067889.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

My first, favorite and most important sequence, the weights of prime numbers: A117078
We see prime numbers classified by level and by weight on the graph.

A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists ➡️ https://oeis.org/A117078

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #3D #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A067259: Cubefree numbers which are not squarefree
A067259 ➡️ https://oeis.org/A067259

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067259.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067259.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067259.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to #decompwlj

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

#math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification